论文标题
曲率和量化的阿诺德陌生感
Curvature and quantized Arnold strangeness
论文作者
论文摘要
通过整合曲率的非平凡密度，我们引入了Arnold Strangentes不可或缺的表达，这是一种著名的平面曲线。关键是Shumakovitch的分区功能，以重新制定Arnold陌生感。我们的集成曲线表明了量化的Arnold陌生性，Taylor的扩展包括旋转数和原始的Arnold陌生感，而且更高的术语是Tabachnikov的不变式。这是Viro对Arnold $ j^ - $的量化的类似物，而Lanzat-Polyak则以$ J^+$为类似。
By integrating curvatures multiplied non-trivial densities, we introduce an integral expression of the Arnold strangeness that is a celebrated plane curve invariant. The key is a partition function by Shumakovitch to reformulate Arnold strangeness. Our integrating curvatures suggests a quantized Arnold strangeness which Taylor expansion includes the rotation number and the original Arnold strangeness, and also higher terms are invariants of Tabachnikov. It is an analogue of the quantization by Viro for Arnold $J^-$ and by Lanzat-Polyak for $J^+$.
